9.4.4.2 CPS in Guile

Guile’s CPS language is composed of continuations. A continuation
is a labelled program point. If you are used to traditional compilers,
think of a continuation as a trivial basic block. A program is a
“soup” of continuations, represented as a map from labels to
continuations.

Like basic blocks, each continuation belongs to only one function. Some
continuations are special, like the continuation corresponding to a
function’s entry point, or the continuation that represents the tail of
a function. Others contain a term. A term contains an
expression, which evaluates to zero or more values. The term also
records the continuation to which it will pass its values. Some terms,
like conditional branches, may continue to one of a number of
continuations.

Continuation labels are small integers. This makes it easy to sort them
and to group them into sets. Whenever a term refers to a continuation,
it does so by name, simply recording the label of the continuation.
Continuation labels are unique among the set of labels in a program.

Variables are also named by small integers. Variable names are unique
among the set of variables in a program.

For example, a simple continuation that receives two values and adds
them together can be matched like this, using the match form from
(ice-9 match):

Here we see the most common kind of continuation, $kargs, which
binds some number of values to variables and then evaluates a term.

CPS Continuation: $kargsnames vars term

Bind the incoming values to the variables vars, with original
names names, and then evaluate term.

The names of a $kargs are just for debugging, and will end
up residualized in the object file for use by the debugger.

The term in a $kargs is always a $continue, which
evaluates an expression and continues to a continuation.

CPS Term: $continuek src exp

Evaluate the expression exp and pass the resulting values (if any)
to the continuation labelled k. The source information associated
with the expression may be found in src, which is either an alist
as in source-properties or is #f if there is no associated
source.

There are a number of expression kinds. Above you see an example of
$primcall.

CPS Expression: $primcallname args

Perform the primitive operation identified by name, a well-known
symbol, passing it the arguments args, and pass all resulting
values to the continuation. The set of available primitives includes
all primitives known to Tree-IL and then some more; see the source code
for details.

The variables that are used by $primcall, or indeed by any
expression, must be defined before the expression is evaluated. An
equivalent way of saying this is that predecessor $kargs
continuation(s) that bind the variables(s) used by the expression must
dominate the continuation that uses the expression: definitions
dominate uses. This condition is trivially satisfied in our example
above, but in general to determine the set of variables that are in
“scope” for a given term, you need to do a flow analysis to see what
continuations dominate a term. The variables that are in scope are
those variables defined by the continuations that dominate a term.

Here is an inventory of the kinds of expressions in Guile’s CPS
language, besides $primcall which has already been described.
Recall that all expressions are wrapped in a $continue term which
specifies their continuation.

CPS Expression: $constval

Continue with the constant value val.

CPS Expression: $primname

Continue with the procedure that implements the primitive operation
named by name.

CPS Expression: $callproc args

Call proc with the arguments args, and pass all values to
the continuation. proc and the elements of the args list
should all be variable names. The continuation identified by the term’s
k should be a $kreceive or a $ktail instance.

CPS Expression: $valuesargs

Pass the values named by the list args to the continuation.

CPS Expression: $branchkt exp

Evaluate the branching expression exp, and continue to kt
with zero values if the test evaluates to true. Otherwise continue to
the continuation named in the outer $continue term.

Only certain expressions are valid in a $branch. Compiling a
$branch avoids allocating space for the test variable, so the
expression should be evaluatable without temporary values. In practice
this condition is true for $primcalls to null?, =,
and similar primitives that have corresponding br-if-foo VM
operations; see the source code for full details. When in doubt, bind
the test expression to a variable, and branch on a $values
expression that references that variable. The optimizer should inline
the reference if possible.

CPS Expression: $promptescape? tag handler

Push a prompt on the stack identified by the variable name tag,
which may be escape-only if escape? is true, and continue with
zero values. If the body aborts to this prompt, control will proceed at
the continuation labelled handler, which should be a
$kreceive continuation. Prompts are later popped by
pop-prompt primcalls.

There are two sub-languages of CPS, higher-order CPS and
first-order CPS. The difference is that in higher-order CPS,
there are $fun and $rec expressions that bind functions or
mutually-recursive functions in the implicit scope of their use sites.
Guile transforms higher-order CPS into first-order CPS by closure
conversion, which chooses representations for all closures and which
arranges to access free variables through the implicit closure parameter
that is passed to every function call.

CPS Expression: $funbody

Continue with a procedure. body names the entry point of the
function, which should be a $kfun. This expression kind is only
valid in higher-order CPS, which is the CPS language before closure
conversion.

CPS Expression: $recnames vars funs

Continue with a set of mutually recursive procedures denoted by
names, vars, and funs. names is a list of
symbols, vars is a list of variable names (unique integers), and
funs is a list of $fun values. Note that the $kargs
continuation should also define names/vars bindings.

The contification pass will attempt to transform the functions declared
in a $rec into local continuations. Any remaining $fun
instances are later removed by the closure conversion pass. By default,
a closure is represented as an object built by a $closure
expression.

CPS Expression: $closurelabel nfree

Build a closure that joins the code at the continuation named
label with space for nfree free variables. The variables
will be initialized later via free-set! primcalls. This
expression kind is part of first-order CPS.

If the closure can be proven to never escape its scope then other
lighter-weight representations can be chosen. Additionally, if all call
sites are known, closure conversion will hard-wire the calls by lowering
$call to $callk.

CPS Expression: $callklabel proc args

Like $call, but for the case where the call target is known to be
in the same compilation unit. label should denote some
$kfun continuation in the program. In this case the proc
is simply an additional argument, since it is not used to determine the
call target at run-time.

At this point we have described terms, expressions, and the most common
kind of continuation, $kargs. $kargs is used when the
predecessors of the continuation can be instructed to pass the values
where the continuation wants them. For example, if a $kargs
continuation k binds a variable v, and the compiler decides
to allocate v to slot 6, all predecessors of k should put
the value for v in slot 6 before jumping to k. One
situation in which this isn’t possible is receiving values from function
calls. Guile has a calling convention for functions which currently
places return values on the stack. A continuation of a call must check
that the number of values returned from a function matches the expected
number of values, and then must shuffle or collect those values to named
variables. $kreceive denotes this kind of continuation.

CPS Continuation: $kreceivearity k

Receive values on the stack. Parse them according to arity, and
then proceed with the parsed values to the $kargs continuation
labelled k. As a limitation specific to $kreceive,
arity may only contain required and rest arguments.

$arity is a helper data structure used by $kreceive and
also by $kclause, described below.

CPS Data: $arityreq opt rest kw allow-other-keys?

A data type declaring an arity. req and opt are lists of
source names of required and optional arguments, respectively.
rest is either the source name of the rest variable, or #f
if this arity does not accept additional values. kw is a list of
the form ((keywordnamevar) ...), describing
the keyword arguments. allow-other-keys? is true if other keyword
arguments are allowed and false otherwise.

Note that all of these names with the exception of the vars in the
kw list are source names, not unique variable names.

Additionally, there are three specific kinds of continuations that are
only used in function entries.

CPS Continuation: $kfunsrc meta self tail clauses

Declare a function entry. src is the source information for the
procedure declaration, and meta is the metadata alist as described
above in Tree-IL’s <lambda>. self is a variable bound to
the procedure being called, and which may be used for self-references.
tail is the label of the $ktail for this function,
corresponding to the function’s tail continuation. clause is the
label of the first $kclause for the first case-lambda
clause in the function, or otherwise #f.

CPS Continuation: $ktail

A tail continuation.

CPS Continuation: $kclausearity cont alternate

A clause of a function with a given arity. Applications of a function
with a compatible set of actual arguments will continue to the
continuation labelled cont, a $kargs instance representing
the clause body. If the arguments are incompatible, control proceeds to
alternate, which is a $kclause for the next clause, or
#f if there is no next clause.